The number is: " 12 ".
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Let "x" represent "the unknown number" (for which we wish to solve.
The expression:
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 = 2 ; Solve for "x" ;
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Method 1)
Add "6" to EACH SIDE of the equation;
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→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 + 6 = 2 + 6 ;
to get:
→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 ;
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Multiply each side of the equation by "
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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→
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
*
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 *
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
;
→ x = 8 *
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
;
=
![\frac{8}{1}](/tpl/images/0092/0491/39134.png)
*
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
;
=
![\frac{8*3}{1*2}](/tpl/images/0092/0491/3320c.png)
;
=
![\frac{24}{2}](/tpl/images/0092/0491/dd41b.png)
;
= 12 .
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x = 12 .
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Method 2)
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![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 = 2 ; Solve for "x" ;
Add "6" to EACH SIDE of the equation;
_______________________________________________
→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 + 6 = 2 + 6 ;
to get:
→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 ;
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Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
→ 3 *
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 * 3 ;
→
![\frac{3}{1}](/tpl/images/0092/0491/89cb8.png)
*
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 * 3 ;
→
![\frac{3*2}{1*3}](/tpl/images/0092/0491/070b6.png)
x = 8 * 3
→
![\frac{6}{3}](/tpl/images/0092/0491/a6483.png)
x = 24 ;
→ 2x = 24 ;
→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :
2x / 2 = 24 / 2 ;
x = 12 .
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Method 3).
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![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x − 6 + 6 = 2 + 6 ;
to get:
→
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x = 8 ;
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Now, divide each side of the equation by "
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
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{
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
x } / {
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
} = 8 / {
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
} ;
to get: x = 8 / {
![\frac{2}{3}](/tpl/images/0092/0491/5f13e.png)
} ;
= 8 * (
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
;
=
![\frac{8}{1}](/tpl/images/0092/0491/8adb5.png)
*
![\frac{3}{2}](/tpl/images/0092/0491/5dd0e.png)
;
=
![\frac{8*3}{1*2}](/tpl/images/0092/0491/3320c.png)
;
=
![\frac{24}{2}](/tpl/images/0092/0491/dd41b.png)
;
= 12 ;
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x = 12 .
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NOTE: Variant: (in "Methods 2 & 3") :
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At the point where:
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= 8 * (
![\frac{3}{2}](/tpl/images/0092/0491/410fe.png)
) ;
=
![\frac{8}{1}](/tpl/images/0092/0491/8adb5.png)
*
![\frac{3}{2}](/tpl/images/0092/0491/5dd0e.png)
;
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We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
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{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
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and we can rewrite the expression:
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![\frac{8}{1}](/tpl/images/0092/0491/8adb5.png)
*
![\frac{3}{2}](/tpl/images/0092/0491/5dd0e.png)
;
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as:
![\frac{4}{1}](/tpl/images/0092/0491/2a287.png)
*
![\frac{3}{1}](/tpl/images/0092/0491/ddba7.png)
;
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which equals:
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→
![\frac{4*3}{1*1}](/tpl/images/0092/0491/ed0f1.png)
;
=
![\frac{12}{1}](/tpl/images/0092/0491/67c96.png)
;
= 12 .
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x = 12 .
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The number is: " 12 ".
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